Watson stepped up to smash home low to Brian Jensen's right.
The visitors were still reorganising at the back when Sinclair collected a short corner to set off an a mazy run down the left.
His chipped cross was half-cleared to Jose Fonte who headed back into the area where 17-year-old Moses was all alone and onside to guide a left-footed strike into the far corner.
In the 37th minute, Morrison skipped round Jensen and pulled the ball back for Soares to slam home from inside the six-yard box.
Palace continued to dominate after the break, and Sinclair made it 4-0 on 61 minutes.
He picked the ball up on the left touchline, cut inside Chris McCann and then burst through two more tired challenges before drilling a low shot past Jensen.
Morrison made it five just four minutes later when Watson again carved open the defence with a run and clever pass.
Morrison kept his cool to slot past Jensen from just inside the area and usher in an exhibition of possession for the remaining 25 minutes.
Crystal Palace manager Neil Warnock: "I can't think of a better achievement in my career. To go from second bottom in November into the play-offs, never mind winning them, is a great effort from all the lads.
"We have a 25% chance now and let's see what happens. It can come down to a lucky break or an individual piece of skill.
"I've won six promotions in my career - but my lucky number is seven."
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